where \(f_0\)  is the standard Fermi function. At the SN interfaces, \(A\)  is the Andreev reflection probablity, \(B\)  is the ordinary reflection probablity, \(T=1-A-B\)  is the transmission probablity [1]}. For \(E<\Delta \)
\(A(E)=\frac{\Delta ^2}{E^2+(\Delta ^2-E^2)(1+2Z_\text{SN}^2)^2},\) 
\(B(E)=1-A(E).\) 
